Cross interpolation for solving high-dimensional dynamical systems on low-rank Tucker and tensor train manifolds

Ghahremani, Behzad; Babaee, Hessam

doi:10.1016/j.cma.2024.117385

Computer Methods in Applied Mechanics and Engineering

2024

DOI: 10.1016/j.cma.2024.117385

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Cross interpolation for solving high-dimensional dynamical systems on low-rank Tucker and tensor train manifolds

Behzad Ghahremani,

Hessam Babaee

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Cited by 2 publications

References 35 publications

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Collocation methods for nonlinear differential equations on low-rank manifolds

Dektor

2025

Linear Algebra and its Applications

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Collocation methods for nonlinear differential equations on low-rank manifolds

Dektor

2025

Linear Algebra and its Applications

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Time-dependent low-rank input–output operator for forced linearized dynamics with unsteady base flows

Amiri-Margavi,

Babaee

2024

J. Fluid Mech.

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Understanding the linear growth of disturbances due to external forcing is crucial for flow stability analysis, flow control, and uncertainty quantification. These applications typically require a large number of forward simulations of the forced linearized dynamics, often in a brute-force fashion. When dealing with simple steady-state or periodic base flows, there exist powerful and cost-effective solution operator techniques. Once these solution operators are constructed, they can be used to determine the response to various forcings with negligible computational cost. However, these methods do not apply to problems with arbitrarily time-dependent base flows. This paper develops and investigates reduced-order modelling with time-dependent bases to build low-rank solution operators for forced linearized dynamics with arbitrarily time-dependent base flows. In particular, we use forced optimally time-dependent decomposition (f-OTD), which extracts the time-dependent correlated structures of the flow response to various excitations. Several demonstrations are included to illustrate the utility of the f-OTD low-rank approximation for performing global transient stability analysis. Additionally, we demonstrate the application of f-OTD in computing the post-transient response of linearized Navier–Stokes equations to a large number of impulses, which has applications in flow control.

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Cross interpolation for solving high-dimensional dynamical systems on low-rank Tucker and tensor train manifolds

Cited by 2 publications

References 35 publications

Collocation methods for nonlinear differential equations on low-rank manifolds

Collocation methods for nonlinear differential equations on low-rank manifolds

Time-dependent low-rank input–output operator for forced linearized dynamics with unsteady base flows

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